Exact and approximate forms of the kinetic energy functional T-s[rho] for molecules obtained via local-scaling transformations

By means of a constructive procedure based on local-scaling transformations, we have obtained the following exact form for the noninteractive kinetic energy functional of general molecular systems: T-s[rho] = Tw[rho] + Sigma(I) integral(Omegat) d(3) r(I)rho(5/3) (r(I)) [1 + r(I) . del(rI) ln lambda(r(I))](-2/3) x [3 + r(I) . del(rI) lnlambda(r(I))](2) [tau(N)(I)(r(I)) + tau(N)(C)(r(I)) + K-N(I)(r(I)) + K-N(C)(r(I))], where lambda(r) is the local-scaling transformation function, T-W[rho] is the von Weiszacker term and tau(N)(l)(r(l)) and kappa(N)(l)(r(l)) are the radial and angular enhancement factors, respectively, within an atomic domain Omega(I). The terms tau(N)(C)(r(l)) and tau(N)(C)(r(l)) (where C stands for complement of I) contain all contributions to the radial and angular enhancement factors within Omega(I) coming from the tails of functions centered on nuclei outside Omega(I.) Also, in the context of an atoms-in-a-molecule approach, we discuss the construction of approximations to the kinetic energy enhancement factors appearing in the previous expression for T-s[rho].